Hi there!
We can begin by solving for the pendulum's velocity at the bottom of its trajectory using the work-energy theorem.
Recall:
[tex]E_i = E_f[/tex]
Initially, we just have Potential Energy. At the bottom, there is just Kinetic Energy.
[tex]PE = KE\\\\[/tex]
Working equation:
[tex]\large\boxed{mgh = \frac{1}{2}mv^2}[/tex]
Rearrange to solve for velocity:
[tex]gh = \frac{1}{2}v^2\\\\v = \sqrt{2gh}\\\\v = \sqrt{2(9.8)(1.5)} = 5.42 \frac{m}{s}[/tex]
Now, we can do a summation of forces:
[tex]\Sigma F = T - W[/tex]
The net force is the centripetal force, so:
[tex]\frac{mv^2}{r} = T - W[/tex]
Rearrange to solve for tension:
[tex]T = \frac{mv^2}{r} + W\\\\T = \frac{5(5.42^2)}{4} + 5(9.8) = \boxed{85.75 N}[/tex]
